Shleck's performance in the 117-mile Alpine section from Station des Rousse to Morzine-Avoriaz, France, left him just 20 seconds behind Evans. Schleck's winning time was 4:54:11.
Defending Tour de France champion Alberto Contador ended in fifth place Sunday, good for third place overall at 61 seconds behind Evans.
The stage also could have marked the end of seven-time champ Lance Armstrong's bid for another title in what he has said is his final Tour de France. The American star tumbled twice during the stretch and had to steer to the side to avoid a crash in the early going.
Sunday's showing dropped Armstrong to 39th overall, 13:26 behind Evans. With those numbers, he is likely out of contention.